Electrode placement for verifying structural intergrity of materials

ABSTRACT

A technique may include applying a first electrical signal to a first pair of drive electrodes, and, while applying the first electrical signal to the first pair of drive electrodes, determining a first measured voltage using a first measurement electrode. The technique further may include applying a second electrical signal to a second pair of drive electrodes, and, while applying the second electrical signal to the second pair of drive electrodes, determining a second measured voltage using a second, different measurement electrode. The first pair of drive electrodes, the second pair of drive electrodes, the first measurement electrode, and the second, different measurement electrode may from a set of N electrodes electrically coupled to the material. The technique also may include determining whether the material includes a crack or other defect based on a comparison between the first measured voltage and the second measured voltage.

TECHNICAL FIELD

The disclosure relates to techniques for verifying structural integrityof conductive or semiconductive matedals.

BACKGROUND

Many materials are useful when their mechanical properties remainintact, but less useful when damaged, such as when cracked. Thus,detection whether these materials are damaged is important. As oneexample, ceramic body plating is used to protect soldiers, policeofficers, and other security personnel from projectiles. Ceramic bodyplating may be useful when undamaged, but may be replaced after beingdamaged, e.g., after cracking.

X-ray scanning, including X-ray radiography and X-ray computedtomography (CT scanning) may be used to detect cracks or other defectsin materials. However, such techniques may utilize large and heavyscanners, which may not be easily portable. Further, X-ray scanning andX-ray CT scanning may be relatively expensive, relatively slow, or both.

SUMMARY

In some examples, the disclosure describes a method for detecting acrack or defect in a material. The method may include applying a firstelectrical signal to a first pair of drive electrodes. The method alsomay include, while applying the first electrical signal to the firstpair of drive electrodes, determining a first measured voltage using afirst measurement electrode. The method further may include applying asecond electrical signal to a second pair of drive electrodes. Themethod additionally may include, while applying the second electricalsignal to the second pair of drive electrodes, determining a secondmeasured voltage using a second, different measurement electrode. Thefirst pair of drive electrodes, the second pair of drive electrodes, thefirst measurement electrode, and the second, different measurementelectrode may from a set of N electrodes electrically coupled to thematerial. The method also may include determining whether the materialincludes a crack or other defect based on a comparison between the firstmeasured voltage and the second measured voltage.

In some examples, the disclosure describes a method for detecting acrack or defect in a material. The method may include, for eachrespective pair of drive electrodes of at least one pair of driveelectrodes electrically coupled to the material, applying an electricalsignal to the respective pair of drive electrodes. The method also mayinclude, for each respective pair of drive electrodes, determining arespective measured voltage using a respective measurement electrode ofa plurality of measurement electrodes while applying the electricalsignal to the respective pair of drive electrodes. Each respectivemeasurement electrode may be substantially symmetrical to anothermeasurement electrode with reference to a symmetry of the material. Theplurality of measurement electrodes are electrically coupled to thematerial. The method further may include determining whether thematerial includes a crack or other defect based on comparisons betweenthe respective measured voltages associated with respective measurementelectrodes that are substantially symmetrical with reference to thesymmetry of the material.

In some examples, the disclosure describes a method for detecting acrack or defect in a material. The method may include, for eachrespective pair of drive electrodes of a plurality of pairs of driveelectrodes electrically coupled to the material, applying a respectiveelectrical signal to the respective pair of drive electrodes. The methodalso may include, for each respective pair of drive electrodes,determining a respective measured voltage using a respective measurementelectrode of a plurality of measurement electrodes while applying theelectrical signal to the respective pair of drive electrodes. Thegeometric configuration of each respective combination of a respectivepair of drive electrodes and a respective measurement electrode isselected so that, in the absence of a crack, each respective measuredvoltage is substantially the same as at least one other respectivemeasured voltage.

In some examples, the disclosure describes a system including a set of Nelectrodes electrically coupled to a material; an electrical signalsource; and a computing device. The computing device may be configuredto cause the electrical signal source to apply a first electrical signalto a first pair of drive electrodes. The computing device also may beconfigured to, while the electrical signal source is applying the firstelectrical signal to the first pair of drive electrodes, determine afirst measured voltage using a first measurement electrode. Thecomputing device further may he configured to cause the electricalsignal source to apply a second electrical signal to a second pair ofdrive electrodes, and, while the electrical signal source is applyingthe second electrical signal to the second pair of drive electrodes,determine a second measured voltage using a second, differentmeasurement electrode. The first pair of drive electrodes, the secondpair of drive electrodes, the first measurement electrode, and thesecond, different measurement electrode may be from the set of Nelectrodes. The computing device additionally may be configured todetermine whether the material includes a crack or other defect based ona comparison between the first measured voltage and the second measuredvoltage.

In some examples, the disclosure describes a system including a set of Nelectrodes electrically coupled to a material; an electrical signalsource; and a computing device. The computing device may be configuredto, for each respective pair of drive electrodes of at least one pair ofdrive electrodes, cause the electrical signal source to apply anelectrical signal to the respective pair of drive electrodes. Thecomputing device also may be configured to, for each respective pair ofdrive electrodes, determine a respective measured voltage using arespective measurement electrode of a plurality of measurementelectrodes while the electrical signal source is applying the electricalsignal to the respective pair of drive electrodes. Each respectivemeasurement electrode is substantially symmetrical to anothermeasurement electrode with reference to the symmetry of the material.The at least one pair of drive electrodes and the plurality ofmeasurement electrodes are from the set of N electrodes. The computingdevice further may be configured to determine whether the materialincludes a crack or other defect based on comparisons between therespective measured voltages associated with respective measurementelectrodes that are substantially symmetrical with reference to thesymmetry of the material.

In some examples, the disclosure describes a system including a set of Nelectrodes electrically coupled to a material; an electrical signalsource; and a computing device. The computing device may be configuredto, for each respective pair of drive electrodes of a plurality of pairsof drive electrodes electrically coupled to the material, cause theelectrical signal source to apply a respective electrical signal to therespective pair of drive electrodes. The plurality of pairs of driveelectrodes are from the set of N electrodes. The computing device alsomay be configured to, for each respective pair of drive electrodes,determine a respective measured voltage using a respective measurementelectrode of a plurality of measurement electrodes while the electricalsignal source is applying the electrical signal to the respective pairof drive electrodes. A geometric configuration of each respectivecombination of a pair of drive electrodes and a respective measurementelectrode is selected so that, in the absence of a crack, eachrespective measured voltage is substantially the same as at least oneother respective measured voltage. The computing device additionally maybe configured to determine whether the material includes a crack orother defect based on comparisons between the respective measuredvoltages.

The techniques described herein may provide one or more advantages. Forexample, using comparisons between multiple voltage measurements from amaterial may allow determination of whether a material includes a crackor other defect without previous measurement of control voltages, whichmay simplify determination of whether the material includes the crack orother defect. As another example, a measurement system as describedherein may offer improved portability and cost compared to an X-rayradiography or X-ray computed tomography system, while offeringsufficient accuracy and detail to enable detection of cracks or otherdefects in a material being used in the field. The details of one ormore examples are set forth in the accompanying drawings and thedescription below. Other features, objects, and advantages will beapparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a conceptual and schematic diagram block illustrating anexample system for determining whether a material includes a crack orother defect based on a comparison between at least a first measuredvoltage associated with the material and a second measured voltageassociated with the material.

FIG. 2 is a conceptual diagram illustrating an example material andarrangement of electrodes on the material.

FIG. 3 is a flow diagram illustrating an example technique fordetermining whether a material includes a crack or other defect based ona comparison between at least a first measured voltage associated withthe material and a second measured voltage associated with the material.

FIGS. 4 and 5 are flow diagrams illustrating example techniques fordetermining whether a material includes a crack or other defect based ona comparison between at least a first measured voltage associated withthe material and a second measured voltage associated with the material.

FIG. 6 is a diagram illustrating an example finite element model of amaterial that includes electrodes positioned on the material.

DETAILED DESCRIPTION

The disclosure describes systems and techniques for verifying structuralintegrity of a material. The techniques may include determining whetherthe material includes a crack or other defect based on a comparisonbetween at least a first measured voltage associated with the materialand a second measured voltage associated with the material. The firstmeasured voltage may be determined by applying an electrical signal to afirst pair of drive electrodes electrically coupled to the material andmeasuring a voltage using a first measurement electrode electricallycoupled to the material. The second voltage may be determined byapplying an electrical signal to a second pair of drive electrodeselectrically coupled to the material and measuring a voltage using asecond measurement electrode electrically coupled to the material. Thefirst measurement electrode used to measure the first measured voltagemay be different than the second measurement electrode used to measurethe second measured voltage. The first pair of drive electrodes and thesecond pair of drive electrodes may be the same or may be different.

The positions of the pair of drive electrodes and the first and secondmeasurement electrodes may be selected to allow meaningful comparisonsbetween the first and second measured voltages. For example, electrodesmay be positioned on the material based on a symmetry of the material,so that each measured voltage is substantially the same when thematerial is intact, or both. As an example, a pair of drive electrodesmay be positioned on a symmetry of the material, and the firstmeasurement electrode and the second measurement electrode may belocated symmetrically with reference to the symmetry. The symmetry mayinclude, for example, a line, a plane, a curve, or a manifold for whicha single mathematical operation made with reference to the symmetry mapsthe first electrode to the second electrode. As another example, a firstpair of drive electrodes may be used to apply the electrical signal usedto measure the first measured voltage via the first electrode, and asecond pair of drive electrodes may be used to apply the electricalsignal used to measure the second measured voltage via the secondelectrode. The first pair of drive electrodes may be symmetrical to thesecond pair of drive electrodes with reference to the symmetry, and thefirst measurement electrode may be symmetrical to the second measurementelectrode with reference to the symmetry. As another example, ageometric configuration of the first pair of drive electrodes and thefirst measurement electrode, and the geometric configuration of thesecond pair of drive electrodes and the second, different measurementelectrode may be selected so that, in the absence of a crack, the firstmeasured voltage is substantially the same as the second measuredvoltage.

By utilizing comparisons between multiple voltage measurements from amaterial may allow determination of whether a material includes a crackor other defect without previous measurement of control voltages, whichmay simplify determination of whether the material includes the crack orother defect. Further, as the multiple voltage measurements areperformed at substantially the same time (e.g., as part of a single setof measurements), the material may be expected to be at substantiallythe same temperature (e.g., the same temperature or nearly the sametemperature). Thus, temperature may be less of a factor in thecomparisons. This may be important for some materials, such assemiconductors, whose conductivity changes significantly as a functionof temperature.

Other techniques also may be used to detect cracks in a material. Forexample, X-ray radiography or X-ray computed tomography (CT) may be usedto detect cracks in a material. However, X-ray radiography and X-ray CTutilize relatively large, relatively expensive equipment to perform thecrack detection. This may prevent X-ray radiography and X-ray CT frombeing portable, such as being used to test materials in the environmentsin which they are used. Moreover, X-ray radiography and X-ray CT may berelatively time consuming.

In contrast, a voltage measurement utilizes relatively smaller,relatively less expensive equipment. As such, the equipment may enableportable crack detection systems, which may be used to detect cracks inmaterials in situ rather than requiring removing the materials to betested to the testing equipment.

FIG. 1 is conceptual and schematic diagram block illustrating an examplesystem 10 for determining presence of a crack or other defect in amaterial 16 based on a comparison between at least a first measuredvoltage associated with the material and a second measured voltageassociated with the material. System 10 of FIG. 1 includes a computingdevice 12, an electrical signal source 14, a plurality of electrodes18A-18L, (collectively, “electrodes 18”), a switch network 20, and anoptional reference electrode 22. Electrodes 18 are electrically coupledto material 16, which is being tested using a four-point voltagemeasurement.

Material 16 may be any material for which detection of a potential crackor other defect is desired. In some examples, material 16 may be anelectrically conductive or an electrically semiconductive material. Forexample, material 16 may include a metal, an alloy, a metalloid, asemiconductor, an electrically conductive or semiconductive ceramic, orthe like. In some examples, material 16 may include a ceramic such asboron carbide (B₄C), silicon carbide (SiC), alumina (Al₂O₃), compositesthereof, or the like.

Material 16 may be used in any one of a wide variety of applications.For example, material 16 may be a ceramic that has relatively highhardness, a relatively high Young's modulus, a relatively high tensilestrength, and may be used in ceramic armor plating. Ceramic armorplating may be used in body armor for military and police personnel,vehicle armor, or the like. Example materials for ceramic armor platinginclude boron carbide (B₄C), silicon carbide (SiC), alumina (Al₂O₃),composites thereof, or the like.

Material 16 may define any geometry, and the geometry of material 16 maybe based at least in part on the intended use for material 16. Forexample, ceramic armor plating may have a geometry defined by thesurface that the armor plating will he applied to. Example geometriesfor material 16 include, but are not limited to, polygonal solids, suchas rectangular solids or solids with more sides.

In some examples, material 16 may define a geometry that has a symmetry,i.e., is symmetric. As used herein, a symmetry is a point, line, plane,curve, or manifold, with reference to which a single mathematicaloperation maps each point of material 16 to another point of material16. In the example of FIG. 1, material 16 includes a plane of symmetry24, across which there is mirror symmetry. As described in furtherdetail below, in some examples in which material 16 includes a symmetry,computing device 12 may compare voltages measured using electrodes orelectrode pairs that are symmetrical with reference to the symmetry,e.g., plane of symmetry 24, to determine whether material 16 includes acrack or other defect.

Electrical signal source 14 may include any device configured to outputan electrical signal to electrodes 18. The electrical signal may includean alternating current (AC) signal or a direct current (DC) signal. Insome examples, electrical signal source 14 may output a current signal;in other examples, electrical signal source 14 may output a voltagesignal. In some examples, electrical signal source 14 may include apower source, such as a battery, a capacitor, a supercapacitor, atransformer electrically connected to a mains voltage, or the like. Insome examples, in addition to the power source, electrical signal source14 may include analog or digital circuitry configured to receive theelectrical signal from the power source and modify the electrical signalinto a format suitable for output to electrodes 18.

Switch network 20 includes a plurality of inputs and a plurality ofoutputs, with respective inputs electrically coupled to each respectiveoutput by the network of switches. For example, switch network 20 mayinclude a pair of inputs electrically coupled to electrical signalsource 14, and at least a pair of inputs electrically coupled tocomputing device 32. Switch network 20 may include at least as manyoutputs are there are electrodes 18 and 22. For example, in the exampleshown in FIG. 1, system 10 includes thirteen electrodes, and switchnetwork 20 thus includes at least thirteen outputs. Each electrode ofelectrodes 18 and reference electrode 22 is electrically coupled to arespective output of switch network 20.

Computing device 12 is configured to control operation of system 10,including electrical signal source 14 and switch network 20. Computingdevice 12 may include any of a wide range of devices, including computerservers, desktop computers, notebook tie., laptop) computers, tabletcomputers, and the like. In some examples, computing device 12 mayinclude a processor. The processor may include one or moremicroprocessors, digital signal processors (DSP), application specificintegrated circuits (ASIC), field programmable gate arrays (FPGA), orother digital logic circuitry. In some examples, computing device 12 mayinclude an analog-to-digital converter (ADC), or system 10 may includean ADC separate from computing device 12. In examples in which the ADCis separate from computing device 12, the ADC may be electricallycoupled between a selected measurement electrode and computing device12. The ADC may measure the voltage using the selected measurementelectrode, under control of computing device 12.

Computing device 12 is communicatively coupled to electrical signalsource 14 and electrically coupled to switch network 20, e.g., eitherdirectly or indirectly via an external device, such as an ADC. Computingdevice 12 may be configured to control electrical signal source 14 tooutput an electrical signal, and may be configured to control switchnetwork 20 to connect a selected pair of electrodes 18 to electricalsignal source 14 to serve as a pair of drive electrodes, such that theelectrical signal output by electrical signal source 14 is output to thepair of drive electrodes.

Computing device 12 is also configured to cause switch network 20 toconnect a selected pair of electrodes 18 or one of electrodes 18 andreference electrode 22 to computing device 12 to serve as a pair ofmeasurement electrodes. In this way, computing device 12 may determine avoltage across a pair of measurement electrodes in response to theelectrical signal output by electrical signal source 14.

Electrodes 18 include a plurality of electrodes electrically coupled tomaterial 16. In some examples, as shown in FIG. 1, each electrode ofelectrodes 18 is also electrically coupled to switch network 20. Each ofelectrodes 18 may be electrically connected to material 16 using anysuitable type of electrical coupling, including, for example, anelectrically conductive adhesive, an electrically conductive solder,embedding electrodes 18 in material 16, a dielectric coupling viacapacitive coupling, or the like.

Electrodes 18 may be attached to any surface of material 16. The surfaceto which electrodes 18 are attached may affect the direction in whichthe electrical field extends and current flows within material 16.Cracks or other defects may affect the magnitude of the voltage moresignificantly when the electrical field and current flow extends acrossa plane of the crack (e.g., normal to a surface of the crack). As such,in some examples, the likely locations of cracks or other defects andthe likely orientation of cracks or other defects within material 16 maybe predicted based on the use for material 16. In some of theseexamples, electrodes 18 may then he attached to material 16 so that theelectrical field and current flow within material 16 extendssubstantially normal to a predicted orientation of the crack or otherdefect.

In some examples, rather than predicting a location of the crack orother defect within material 16 and placing electrodes 18 based on theprediction, electrodes 18 may he attached to more than one surface ofmaterial 16. For example, if material 16 is in the shape of a cube,electrodes 18 may be attached to three orthogonal surfaces of the cube.By attaching a respective electrode of electrodes 18 to three orthogonalsurfaces, the electrical field and current flow may be caused to extendin one of three orthogonal directions depending on the electrodes 18through which the electrical signal is applied. This may increase alikelihood that induced the electrical field and current flow willextend within material 16 normal to the plane of any crack in material16. Other examples are possible for other shapes. In some examples,electrodes 18 are distributed across a surface area of material 16, asshown in FIG. 1. In other examples, electrodes 18 are distributed arounda perimeter of material 16. In some examples, plurality of electrodes 18may be referred to as a set of N electrodes 18.

In some examples, electrodes 18 may be positioned on material 16according to a selected geometric relationship, to achieve a selectedrelationship between voltages measured using electrodes 18, or both. Forexample, electrodes 18 may be positioned on material 16 so that eachelectrode of electrodes 18 is substantially symmetric to another one ofelectrodes 18 with reference to the symmetry of material 16. In theexample of FIG. 1, first electrode 18A is substantially symmetric tosixth electrode 18F with reference to plane of symmetry 24, secondelectrode 18B is substantially symmetric to fifth electrode 18D withreference to plane of symmetry 24, third electrode 18C is substantiallysymmetric to fourth electrode 18D with reference to plane of symmetry24, seventh electrode 18G is substantially symmetric to twelfthelectrode 18L with reference to plane of symmetry 24, eighth electrode18H is substantially symmetric to eleventh electrode 18K with referenceto plane of symmetry 24, and ninth electrode 181 is substantiallysymmetric to tenth electrode 18J with reference to plane of symmetry 24.

As another example, electrodes 18 may be positioned on material 16 sothat a respective pair of electrodes is substantially symmetric toanother respective pair of electrodes 18 with reference to the symmetryof material 16. For example, a first pair of electrodes may includefirst electrode 18A and twelfth electrode 18L and a second pair ofelectrodes may include sixth electrode I8F and seventh electrode 18G.The first pair of electrodes is symmetric to the second pair ofelectrodes with reference to plane of symmetry 24. Similarly, a thirdpair of electrodes may include second electrode 18B and eleventhelectrode 18K and a fourth pair of electrodes may include fifthelectrode 18E and eighth electrode 18I. The third pair of electrodes issymmetric to the fourth pair of electrodes with reference to plane ofsymmetry 24. Additionally, a fifth pair of electrodes may include thirdelectrode 18C and tenth electrode 18J and a sixth pair of electrodes mayinclude fourth electrode 18D and ninth electrode 181. The fifth pair ofelectrodes is symmetric to the sixth pair of electrodes with referenceto plane of symmetry 24.

In some examples, electrodes 18 may be positioned on material 16 so thateach respective pair of electrodes is substantially symmetric to anotherrespective pair of electrodes 18 with reference to the symmetry ofmaterial 16. This may be accomplished in examples in which eachelectrode of electrodes 18 is substantially symmetric to another one ofelectrodes 18 with reference to the symmetry of material 16, and arespective electrode of two symmetric electrodes is used in eachrespective pair of electrodes in a symmetric pair of electrodes.

Although not shown in FIG. 1, in some examples, two electrodes may bepositioned on the symmetry of material 16, e.g., on plane of symmetry 24shown in FIG. 1. For example, FIG. 2 is a conceptual diagramillustrating an example material 32 and arrangement of electrodes E0-E15on material 32. Material 32 includes a plane of symmetry 34. Twoelectrodes, E0 and E8, are positioned on plane of symmetry 34 atopposite ends of material 32. The remainder of electrodes E0-E15 arepositioned on material 32 so that an equal number of electrodes are oneach side of plane of symmetry 34 and each respective electrode on oneside of plane of symmetry 34 is symmetric to a respective electrode onthe other side of plane of symmetry 34. For example, electrodes E7 andE9 are symmetric with reference to plane of symmetry 34, electrodes E6and E10 are symmetric with reference to plane of symmetry 34, electrodesE5 and E11 are symmetric with reference to plane of symmetry 34,electrodes E4 and E12 are symmetric with reference to plane of symmetry34, electrodes E3 and E13 are symmetric with reference to plane ofsymmetry 34, electrodes E2 and E14 are symmetric with reference to planeof symmetry 34, and electrodes E1 and E15 are symmetric with referenceto plane of symmetry 34.

FIG. 2 also includes labels for gaps between respective electrodes ofelectrodes E0-E15. For example, the gap from E0 to D1 is labeled H, thegap from E1 to E2 is labeled G. the gap from E2 to E3 is labeled F, thegap from E3 to E4 is labeled E, the gap from E4 to E5 is labeled D, thegap from E5 to E6 is labeled C, the gap from E6 to E7 is labeled B, andthe bap from E7 to E8 is labeled A. The mirror image gaps on the rightside of plane of symmetry 34 are labeled with similar letters and aprime designation. As electrodes E0-E15 are placed symmetrically withreference to plane of symmetry 34, voltages measured for correspondinggaps on opposite sides of plane of symmetry 34 may be substantially thesame in the absence of a crack or defect in material 32, assuming thatelectrodes E0 and E8 are used as the pair of drive electrodes, or thattwo pairs of drive electrodes that are symmetric to each other withreference to line of symmetry 34 are used during measurement of thevoltages.

Positioning electrodes 18 to be exactly symmetrical may be difficult toachieve in practice. Hence, electrodes 18 may be positioned to besubstantially symmetrical. As used here, substantially symmetrical meansthat the electrodes are placed approximately symmetrical with referenceto a symmetry of material 16, e.g., within about 0.5 mm of beingsymmetric, within about 0.2 mm of being symmetric or within about 0.1 mmof being symmetric.

In some examples, rather than electrodes 18 being positioned based onsymmetry of material, electrodes 18 may be positioned to achieve aselected relationship between voltages measured using electrodes 18. Forexample, electrodes 18 may be positioned to achieve measurement of asubstantially similar voltage (e.g., the same or nearly the samevoltage) in the absence of a crack or other defect. In some examples,this may include positioning respective groups of electrodes to achievemeasurement of a substantially similar voltage (e.g., the same or nearlythe same voltage) in the absence of a crack or other defect. Eachrespective group of electrodes may include a pair of drive electrodesand one or two measurement electrodes. For example, a group ofelectrodes may include a pair of drive electrodes separated by one ortwo measurement electrodes. Using electrodes 18 shown in FIG. 1, anexample of this configuration may include a pair of drive electrodesthat includes first electrode 18A and fourth electrode I8D, and a pairof measurement electrodes that includes second electrode 18B and thirdelectrode I8C. Another example of this configuration may include a pairof drive electrodes that includes first electrode 18A and thirdelectrode 18C, and a measurement electrode that includes secondelectrode 18B (to measure a single-ended voltage using second electrode18B and reference electrode 22).

In some examples, each group of electrodes may not share any electrodeswith each other group of electrodes. In other examples, each group ofelectrodes may share one or more electrodes with another group ofelectrodes. For example, a first group of electrodes may include firstelectrode 18A and fourth electrode 18D as a pair of drive electrodes,and may include second electrode 8B and third electrode 18C as a pair ofdrive electrodes. A second group of electrodes may include secondelectrode 18B and fifth electrode 18E as a pair of drive electrodes, andthird electrode 18C and fourth electrode 18D as a pair of measurementelectrodes. In other words, each group of electrodes may include fourelectrodes, the two outer electrodes being drive electrodes and the twoinner electrodes being measurement electrodes. Each respective group ofelectrodes may be formed by four adjacent electrodes, and eachsubsequent group may be formed by shifting the group to an adjacentelectrode in a selected pattern (e.g., left or right, clockwise orcounterclockwise, or the like). In some examples, the number of groupsof electrodes may equal the number of electrodes 18. In examples such asthis, the placement of each electrode of electrodes 18 may be selectedso that the voltage measured using each respective group of electrodesis substantially the same as the voltage measured using each otherrespective group of electrodes.

In some examples, positioning electrodes 18 so that the voltage measuredusing each respective group of electrodes is exactly the same as thevoltage measured using each other respective group of electrodes may bedifficult to achieve in practice. Hence, electrodes 18 may be positionedto be so that the voltage measured using each respective group ofelectrodes is substantially the same as the voltage measured using eachother respective group of electrodes. As used here, substantially thesame means that the electrodes are placed so that the voltage measuredusing each respective group of electrodes is within a threshold amountas the voltage measured using each other respective group of electrodesin the absence of a crack or defect in material 16. The threshold amountmay be a predetermined percentage of the measured voltage, such as, forexample, 20%, 10%, 5%, or 1%.

In some examples, electrodes 18 may be positioned so that the voltagemeasured using each respective group of electrodes is substantially thesame as the voltage measured using each other respective group ofelectrodes by using experimental iteration. For example, a first groupof electrodes may be positioned based on geometry of material 16 toaccomplish current distribution within a selected volume of material 16.For instance, the first group of electrodes may be positioned near acorner or edge of material 16 to improve uniform current distributionthroughout material 16 near the corner or edge. Each subsequentelectrode 18 or group of electrodes 18 may be positioned so that thevoltage measured using the group or groups of electrodes of which theelectrode is a part is substantially the same as the voltage measuredusing the first group. If, on first positioning of the subsequentelectrode 18 or group of electrodes 18, the voltage measured using thesubsequent electrode 18 or group of electrodes 18 is not substantiallythe same as the voltage measured using the first group of electrodes,the subsequent electrode 18 or group of electrodes 18 may berepositioned to achieve a more similar voltage measurement. This processmay be repeated for each subsequent electrode of electrodes IS.

In other examples, instead of using experimental positioning, theplacement of electrodes 18 may be determined (e.g., by computing device12 or another computing device) using a physics-based simulation tool.For example, computing device 12 may be programmed with a finite elementmodel (FEM) of material 16 which implements the physics-basedsimulation. The FEM of material 16 may include substantially accurate(e.g., accurate or approximately accurate) geometry of material 16(e.g., the shape and volume of material 16), and also may includelocations of electrodes 18 attached to material 16. In some examples,the FEM of material 16 may additionally include representativeproperties of material 16, including, for example, conductivity,resistivity, other related electrical properties, and the like. The FEMof material 16 may include representative properties of material 16 foreach respective node representing material 16. For each group ofelectrodes, computing device 12 may simulate applying an electricalsignal to a respective pair of drive electrodes and determine asimulated measured voltage using a respective pair of measurementelectrodes. Computing device 12 may compare measured voltages fromadjacent groups of electrodes, and adjust positioning of one or more ofelectrodes 18 based on the comparison. Computing device 12 may iteratethis process until each measured voltage is within a threshold amount,e.g., 20%, 10%, 5%, 1%, or the like. The positions of electrodes 18determined by computing device 12 then may be used to place electrodes18 on material 16. In some examples, electrodes 18 may be positioned onmaterial 16 to satisfy both symmetry and substantially equal measuredvoltages. To accomplish this, the following technique may he used insome examples. The technique may be implemented either experimentally,e.g., using system 10 of FIG. 1, or theoretically, e.g., using thephysics-based model described above. First, two of electrodes 18 may bepositioned on the symmetry of material 16, e.g., on plane of symmetry 24shown in FIG. 1. An equal number of electrodes 18 then may be positionedon either side of the symmetry of material 16, such that the additionalelectrodes 18 result in symmetry of electrodes 18 with reference to thesymmetry of material 16.

Computing device 12 then may determine measured voltages for each groupof electrodes. In some examples, electrodes 18 may be numberedsequentially around the perimeter of material 16, e,g, first electrode18A is 1, second electrode 18B is 2, third electrode 18C is 3, and thelike. For each integer 1 to N, where N is the number of electrodes (12in the example of FIG. 1), a group of electrodes may include a pair ofdrive electrodes X and X+3, and a pair of measurement electrodes X+1 andX+2. There may be the same number of groups of electrodes as electrodes18, such that the groups of electrodes eventually wrap around theperimeter of material 16. Thus, computing device may determine the samenumber of measured voltages as there are electrodes 18 (12 in theexample of FIG. 1).

Computing device 12 then may determine a minimum measured voltage forthe 12 measured voltages and determine the electrode numbers of the pairof measurement electrodes associated with the minimum voltage. Computingdevice 12 also may determine the measured voltages for the pairs ofmeasurement electrodes on either side of the pair of measurementelectrodes associated with the minimum measured voltage. For example, ifthe minimum measured voltage is between third electrode 18C and fourthelectrode 18D, computing device 12 may determine the measured voltagebetween second electrode 18B and third electrode 18C, and the measuredvoltage between fourth electrode 18D and fifth electrode 18E. Computingdevice 12 may determine which voltage between the measured voltages oneither side of the minimum measured voltage is larger. Computing device12 then may identify the common electrode from the pair of electrodesassociated with the minimum measured voltage and the pair of electrodesassociated with the larger measured voltage between the pairs ofmeasurement electrodes on either side of the pair of measurementelectrodes associated with the minimum measured voltage. In examples inwhich computing device 12 is determining the position of electrodesusing the physics-based model, computing device 12 may move the commonelectrode away from the other electrode in the pair of electrodesassociated with the minimum value by a predetermined distance. Inexamples in which positioning of electrodes 18 is being determinedexperimentally, computing device 12 may output the measured voltages andassociated pairs of measurement electrodes determined in this technique,or may output an indication of the electrode to be moved, and anoperator may move the electrode on material 16 by the predetermineddistance. Further, as electrodes 18 are positioned symmetrically onmaterial 16, the electrode that is symmetric to the electrode that ismoved also may be moved to maintain symmetry of electrodes 18.

Computing device 12 may repeat these steps until all measured voltagesare within a threshold amount of each other (e.g., 20%, 10%, 5%, or 1%),or until improvement in similarity of the measured voltages falls belowa threshold amount (e.g., 0.1% or the like).

In some examples, system 10 may optionally include reference electrode22, which may not be electrically coupled to material 16 and may be usedfor single-ended voltage measurements between one electrode of pluralityof electrodes 18 and reference electrode 22. Reference electrode 22 maybe at a selected voltage, such a ground or an offset voltage. In someexamples, computing device 12 may use the single-ended voltages in thetechniques described herein to determine whether material 16 includes acrack or other defect. In other examples, computing device 12 maydetermine differential voltages between two electrodes electricallycoupled to material 16 by comparing (e,g, subtracting) single endedvoltages associated with the two electrodes, and computing device 12 mayuse these differential voltages in the techniques described herein todetermine whether material 16 includes a crack or other defect. In stillother examples, computing device 12 may determine a voltage between twoof electrodes 18 directly, e.g., without first determining twosingle-ended voltages.

By positioning electrodes 18 according to a selected geometricrelationship, to achieve a selected relationship between voltagesmeasured using electrodes 18, or both, computing device 12 may determinewhether material 16 includes a crack or other defect based on acomparison between at least a first measured voltage associated withmaterial 16 and a second measured voltage associated with material 16.The first and second measured voltages may be measured during a singleset of measurements, e.g., at substantially the same time. This mayoptionally allow determination of whether material 16 includes a crackor defect without previous measurement of control voltages, may, in someexamples, provide a large number of measured voltages to which anymeasured voltage may be compared, or the like. This may simplifydetermination of whether material 16 includes the crack or other defect,may improve accuracy (e.g., increase true positives, increase truenegatives, decrease false positives, decrease false negatives, orcombinations thereof) of detection of cracks or other defects, or thelike. Further, as the multiple voltage measurements are performed atsubstantially the same time (e.g., as part of a single set ofmeasurements), the material may be expected to be at substantially thesame temperature (e.g., the same temperature or nearly the sametemperature). Thus, temperature may be less of a factor in thecomparisons. This may be important for some materials, such assemiconductors, whose conductivity changes significantly as a functionof temperature.

FIG. 3 is a flow diagram illustrating an example technique fordetermining whether a material includes a crack or other defect based ona comparison between at least a first measured voltage associated withthe material and a second measured voltage associated with the material.The technique of FIG. 3 will be described with concurrent reference tosystem 10 of FIG. 1, but it will be understood that other systems thatinclude more or fewer components than system 10 may perform thetechnique of FIG. 3 (e.g., a system that includes only computing device12), and that system 10 may be used to perform other techniques (e.g.,the techniques of FIGS. 4 and 5, among other techniques).

The technique of FIG. 3 may include applying a first electrical signalto a first pair of drive electrodes (42). For example, computing device12 may cause switch network 20 to electrically couple a pair ofelectrodes 18 to electrical signal source 14 as a pair of driveelectrodes. Computing device 12 then may cause electrical signal source14 to output an electrical signal, such as a current signal or a voltagesignal, which is conducted across material 16 between the pair of driveelectrodes 18.

The technique of FIG. 3 also includes determining, by computing device12, a first measured voltage using a first measurement electrode (44).To determine the first measured voltage using the first measurementelectrode (44), computing device 12 may cause switch network 20 toelectrically couple a pair of electrodes to computing device 12 (oranother device, such as an ADC) to be a pair of measurement electrodes.As described above, in some examples, the pair of measurement electrodesmay include two of electrodes 18, each of which is not a driveelectrode. In some examples, the two of electrodes 18 may be physicallyadjacent to each other on material 16.

In other examples, the pair of measurement electrodes may includereference electrode 22 and one of electrodes 18. In examples in whichthe pair of measurement electrodes includes reference electrode 22 andone of electrodes 18, computing device 12 may determine the firstmeasured voltage between reference electrode 22 and a first one ofelectrodes 18. In still other examples, computing device 12 may causeswitch network 20 to connect a first electrode of electrodes 18 andreference electrode 22 to computing device 12 (or another device, suchas an ADC) to be a first pair of measurement electrodes, may measure afirst voltage using the first electrode and reference electrode 22, maycause switch network 20 to connect a second electrode of electrodes 18and reference electrode 22 to computing device 12 (or another device,such as an ADC) to he a second pair of measurement electrodes, maymeasure a second voltage using the first electrode and referenceelectrode 22, and may determine a difference between the first voltageand the second voltage to determine the first measured voltage.Regardless of the particular implementation, computing device 12 maydetermine a voltage between the measurement electrodes while electricalsignal source 14 is applying, the electrical signal to material 16 viathe pair of drive electrodes.

The technique of FIG. 3 also includes applying a second electricalsignal to a second pair of drive electrodes (46). For example, computingdevice 12 may cause switch network 20 to electrically couple a pair ofelectrodes 18 to electrical signal source 14 as a pair of driveelectrodes. Computing device 12 then may cause electrical signal source14 to output an electrical signal, such as a current signal or a voltagesignal, which is conducted across material 16 between the pair of driveelectrodes 18. In sonic examples, the first pair of drive electrodes andthe second pair of drive electrodes may be the same. For example, bothof the pairs of drive electrodes may be on a plane of symmetry 24 ofmaterial 16 (e.g., as are electrodes E0 and E8 in FIG. 2). In otherexamples, the first pair of drive electrode and the second pair of driveelectrodes may be different.

The technique of FIG. 3 also includes determining, by computing device12, a second measured voltage using a second measurement electrode (44).The second measurement electrode may be different than the firstmeasurement electrode. Computing device 12 may determine the secondmeasured voltage using any of the techniques described above withreference to the first measured voltage.

In some examples, the geometrical configuration of the first pair ofdrive electrodes, the second pair of drive electrodes, the firstmeasurement electrode, and the second measurement electrode may beselected to allow meaningful comparisons between the first measuredvoltage and the second measured voltage. For example, the first pair ofdrive electrodes and the second pair of drive electrodes may be the samepair of electrodes, and may be positioned on the symmetry of material16, e.g., on plane of symmetry 24. The first measurement electrode andsecond measurement electrode may be positioned symmetrically withreference to the symmetry of material 16, e.g., with reference to planeof symmetry 24. In such example, the first measured voltage and thesecond measured voltage should be substantially the same (e.g., the sameor nearly the same) in the absence of a crack or other defect inmaterial 16. For example, in the absence of a crack or defect inmaterial 16, the first voltage and the second voltage may be within apredetermined percentage of each other, such as, for example, withinabout 20%, 10%, 5%, or 1% of each other.

As another example, the first pair of drive electrodes and the secondpair of drive electrodes may be the different than each other. The firstpair of drive electrodes and the first measurement electrode are a firstgroup of electrodes and the second pair of drive electrodes and thesecond measurement electrode are a second group of electrodes. The firstand second group of electrodes may he symmetric with each other relativeto the symmetry of material 16, e.g., plane of symmetry 24. For example,the first group of electrodes may include a pair of drive electrodesthat includes first electrode 18A and third electrode 18C and ameasurement electrode that is second electrode 18B, and the second groupof electrodes may include a pair of drive electrodes that includesfourth electrode 18D and sixth electrode 18F and a measurement electrodethat is fifth electrode 18E. The first group of electrodes is symmetricto the second group of electrodes with reference to plane of symmetry24. As such, in the absence of a crack or other defect in material 16the first measured voltage and the second measured voltage should besubstantially the same (e.g., the same or nearly the same).

As a further example, electrodes 18 may be positioned so that, for eachgroup that includes a pair of drive electrodes and a measurementelectrode, the measured voltage in the absence of a crack or otherdefect is substantially the same. The respective groups of electrodesmay or may not be symmetric to another group of electrodes, and material16 may or may not include a symmetry. As such, regardless of the groupsof electrodes selected as the first group of electrodes and the secondgroup of electrodes, in the absence of a crack or other defect inmaterial 16 the first measured voltage and the second measured voltagemay be substantially the same (e.g., the same or nearly the same).

The technique of FIG. 3 also includes determining, by computing device12, whether material 16 includes a crack or other defect based on thefirst and second measured voltages (50). As described above, because ofhow electrodes 18 are placed and how computing device 12 selects pairsof drive electrodes and measurement electrodes, the first and secondmeasured voltages are substantially the same in the absence of a crackor other defect in material 16. As such, computing device 12 may comparethe first measured voltage and the second measured voltage, and, inresponse to the first and second measured voltages being substantiallythe same (e.g., within a threshold amount of each other) may determinethat material 16 does not include a crack or other defect. On the otherhand, in response to the first and second measured voltages not beingsubstantially the same (e.g., different than each other by more than athreshold amount), computing device 12 may determine that material 16includes a crack or other defect. The threshold amount may be the sameor slightly greater than the threshold amount used to determine theposition of electrodes 18. For example, the threshold amount may be 1%,5%, 10%, 20%, or the like. Computing device 12 may compare the first andsecond measured voltages by subtracting one of the first or secondmeasured. voltages from the other of the first or second measured.voltages, by taking a ratio of one of the first or second measured.voltages from the other of the first or second measured voltages, or thelike, and then determining a percentage difference between the first orsecond measured voltages.

In some examples, in addition to comparing the first and second measuredvoltages, computing device 12 may utilize control voltages to determinewhether material 16 includes a crack or other defect based on the firstand second measured voltages (50). The control voltage may represent thevoltage measured for a give combination of pair of drive electrodes andmeasurement electrode when material 16 does not include a crack or otherdefect. The control voltage may be based on material 16, a model, or anaverage of a plurality of materials that are similar to or substantiallythe same as material 16. For example, computing device 12 or anothersimilar computing device may determine the control voltage at a time atwhich material 16 is manufactured, or a time at which an independentmeasurement (e.g., X-ray radiology or X-ray CT scan) may be used toverify that material 16 is intact, undamaged, or does not include acrack. Computing device 12 or the other similar computing device maydetermine by control voltage by applying the electrical signal to a pairof drive electrodes from electrodes 18 and determining the measuredvoltage using a measurement electrode. In some examples, the controlvoltages may be determined using similar or substantially the samecombinations of pairs of drive electrodes and measurement electrodes asare used to determine the measured voltages described above.

In other examples, the control voltage may be determined using a modelof the material in an intact (undamaged) state. For example, computingdevice 12 may execute the model of material 16 and determine the controlvoltage based on the model. In some examples, the model may include aphysics-based model of the electrical properties of material 16. In someother examples, the control voltage may be determined as an average(e.g., mean) of a plurality of similar materials (e.g., in geometry andcomposition) that are known to he intact (undamaged). This controlvoltage may be stored (e.g., in a memory device associated withcomputing device 12) for later use.

In examples in which computing device 12 utilizes control voltages,computing device 12 may first compare the first measured voltage to afirst control voltage and compare the second measured voltage to asecond control voltage. The first control voltage may be associated withthe same combination of drive electrodes and measurement electrode asthe first measured voltage, and the second control voltage may beassociated with the same combination of drive electrodes and measurementelectrode as the second measured voltage. The comparison between therespective measured voltage and the respective control voltage mayinclude subtracting the respective control voltage from the respectivemeasured voltage or dividing by respective measured voltage by therespective control voltage. By utilizing control voltages in thismanner, the technique may account for variations between the respectivevoltages that exist even in the absence of cracks or other defects. Forexample, as described above, the first and second voltage may be withina threshold amount of each other in the absence of a crack or otherdefect, but this threshold amount may be, in some examples, as large asabout 20%. Hence, there may still be variations between voltages even ifthe absence of cracks or other defects. As the control voltagesrepresent electrical behavior of material 16 in the absence of cracks orother defects, the control voltages may help account for the variationsin voltages between measurement electrodes or groups of electrodes.

After the respective measured voltages have been compared to therespective control voltages, the results of the respective comparisons(e.g., the differences or ratios) may be compared to determine whethermaterial 16 includes a crack or other defect according to the techniquesdescribed above.

FIG. 4 is a flow diagram illustrating another example technique fordetermining whether a material includes a crack or other defect based ona comparison between at least a first measured voltage associated withthe material and a second measured voltage associated with the material.The technique of FIG. 4 will be described with concurrent reference tosystem 10 of FIG. 1, but it will be understood that other systems thatinclude more or fewer components than system 10 may perform thetechnique of FIG. 4 (e.g., a system that includes only computing device12), and that system 10 may be used to perform other techniques (e.g.,the techniques of FIGS. 3 and 5, among other techniques).

The technique of FIG. 4 includes applying an electrical signal to afirst pair of drive electrodes electrically coupled to material 16 (52).For example, computing device 12 may cause switch network 20 toelectrically couple electrical signal source 14 to a selected pair ofelectrodes 18, which serves as a pair of drive electrodes. The selectedpair of electrodes 18 may include any two electrodes of electrodes 18.In some examples, the selected pair of electrodes 18 may be adjacent toeach other; in other examples, the selected pair of electrodes may bespaced apart. For example, in some instances, the selected pair ofelectrodes 18 may be substantially opposite each other in the array ofelectrodes, e.g., electrode 18A and electrode 18L or electrode 18F andelectrode 18G, or may be separated by a predetermined number ofelectrodes 18, e.g., separated by two electrodes of electrodes 18. Insome examples, the pair of electrodes 18 may include two electrodes thatare disposed on a symmetry of material 16, e.g., electrodes E0 and E8disposed on plane of symmetry 34 in FIG. 2.

Computing device 12 then may cause electrical signal source 14 to applythe electrical signal to the first pair of drive electrodes electricallycoupled to material 16 (52), e.g., via switch network 20. The electricalsignal may include an AC signal or a DC signal, and may include acurrent signal or a voltage signal. In sonic examples, the type ofelectrical signal may depend on the composition of material 16. Forexample, a DC signal may be used to measure a voltage of an electricallyconductive or electrically semiconductive material, while an AC signalmay be used to measure a voltage of an electrically conductive material,an electrically semiconductive material, or a dielectric material.Computing device 12 also may control electrical signal source 14 togenerate the predetermined electrical signal with a selected amplitude,duration, frequency, and other signal characteristics.

The technique of FIG. 4 also includes, while applying the electricalsignal to the first pair of drive electrodes, determining a measuredvoltage using a measurement electrode electrically coupled to material16 (54). For example, computing device 12 may cause switch network 20 toelectrically couple computing device 12 to a selected pair ofmeasurement electrodes. The selected pair of measurement electrodes mayhe any two electrodes from electrodes 18, neither of which is being usedas one of the electrodes in the drive pair of electrodes, or may bereference electrode 22 and any one of electrodes 18 that is not beingused as one of the electrodes in the drive pair of electrodes. In someexamples, the two electrodes in the pair of measurement electrodes maybe adjacent to each other, e.g., electrode 18B and electrode 18C, orelectrode 18D and electrode 18J. In other examples, the two electrodesin the pair of measurement electrodes may be spaced each other with oneor more electrodes between, e.g., electrode 18B and electrode 18D, orelectrode 18E and electrode 18H. Using adjacent electrodes as the pairof measurement electrodes may result in a higher signal-noise-ratio inthe voltage measurement, but may reduce an area of material 16 for whichthe voltage is measured. Regardless of the particular electrodes coupledto computing device 12, computing device 12 may determine a voltageusing the measurement electrode (54) while electrical signal source 14is applying the electrical signal to the selected pair of driveelectrodes (52).

In some examples, computing device 12 may be configured to determine arespective measured voltage for a plurality of measurement electrodesfor each pair of drive electrodes. Hence, in some examples, thetechnique of FIG. 4 further includes determining whether there is anadditional measurement electrode for which to determine a measuredvoltage (56) for the selected pair of drive electrodes. In response todetermining that there is an additional electrode to be used as ameasurement electrode (the “YES” branch of decision block 56), computingdevice 12 may cause switch network 20 to couple the selected electrodeto computing device 12. Computing device 12 then may determine ameasured-voltage using the selected measurement electrode (54).

Computing device 12 may repeat this determination (56), coupling of aselected measurement electrode to computing device 12 using switchnetwork 20, and determination of a respective measured voltage (54)until computing device 12 determines there are no additional electrodes18 to be used as a measurement electrode for the selected pair of driveelectrodes (the “NO” branch of decision block 56).

In some examples, the technique of FIG. 4 optionally includesdetermining, by computing device 12, whether there is an additional pairof drive electrodes to which to apply the electrical signal (58). Forexample, computing device 12 may be configured to utilize each uniquepair of electrodes or each unique pair of electrodes separated by apredetermined number of electrodes (e,g., two electrodes) as a pair ofdrive electrodes. In other examples, only a single pair of electrodes 18may be utilized as a pair of drive electrodes, and the technique of FIG.4 may not include determining, by computing device 12, whether there isan additional pair of drive electrodes to which to apply the electricalsignal (58).

In examples in which the technique of FIG. 4 includes determining, bycomputing device 12, whether there is an additional pair of driveelectrodes to which to apply the electrical signal (58), upon selectinga new pair of drive electrodes (the “YES” branch of decision block 58),computing device 12 may control switch network 20 to electrically couplethe selected pair of drive electrodes to electrical signal source 14.Computing device 12 then may cause electrical signal source 14 to applythe electrical signal to the new selected pair of drive electrodes (52).Computing device then may cause switch network 20 to electrically couplecomputing device 12 to a selected measurement electrode, and maydetermine a respective measured voltage using the selected measurementelectrode (54). Again, computing device 12 may determine whether thereis an additional measurement electrode with which to measure a measuredvoltage (56) for the selected pair of drive electrodes. In response todetermining that there is an additional electrode to be used as ameasurement electrode (the “YES” branch of decision block 56) for theselected pair of drive electrodes, computing device 12 may controlswitch network 20 to couple the selected electrode to computing device12 as a measurement electrode. Computing device 12 then may determine ameasured voltage using the selected measurement electrode. Computingdevice 12 may repeat this determination (56), coupling of selectedmeasurement electrodes to computing device 12 using switch network 20,and determination of a respective measured voltage (54) until computingdevice 12 determines there are no additional electrodes 18 to be used asmeasurement electrodes for the selected pair of drive electrodes (the“NO” branch of decision block 56).

Computing device 12 then may determine whether there is an additionalpair of electrodes 18 to be used as a pair of drive electrodes (58).Computing device 12 may repeat this algorithm until computing device 12determines there are no more additional pairs of electrodes 18 to beused as a pair of drive electrodes (the “NO” branch of decision block58).

Once computing device 12 has determined that there are no additionalpairs of electrodes 18 to be used as a pair of drive electrodes (the“NO” branch of decision block 58), computing device 12 may determinewhether material 16 includes a crack or other defect based on respectivemeasured voltages associated with respective measurement electrodes thatare substantially symmetrical with reference to the symmetry of material16 (60).

For example, referring to FIG. 2, electrodes E0 and E8 may be used theonly pair of drive electrodes, and computing device 12 may determinemeasurement voltages for each of electrodes E1-E7 and E9-E15. Computingdevice 12 may utilize single-ended voltages associated with eachrespective electrode of electrodes E1-E7 and E9-E15, may determinedifferential voltages between adjacent electrodes of electrodes E1-E7and E9-E15, or may directly measure differential voltages betweenadjacent electrodes of electrodes E1-E7 and E9-E15. In some examples,computing device 12 also may measure or determine voltages between E15and E), between E0 and E1, between E7 and E8, and between E8 and E9.

Computing device 12 then may compare respective measured voltagesassociated with respective measurement electrodes or respectivemeasurement electrode pairs that are symmetric with reference to planeof symmetry 34. For example, computing device 12 may compare themeasured voltage associated with E1 and the measured voltage associatedwith E15, as E1 and E15 are symmetric with reference to plane ofsymmetry 34. Similarly, in examples in which computing device 12measures or determines differential voltages, computing device 12 maycompare a measured voltage associated with electrode pair E1 and E2 anda measured voltage associated with electrode pair E15 and E14. Material32 includes a number of symmetric electrodes or electrode pairs, andcomputing device 12 may compare at least some voltages associated withsymmetric electrodes or electrode pairs or all voltages associated withsymmetric electrodes or electrode pairs to determine whether material 16or 32 includes a crack or other defect.

In some examples, rather than using only a pair of electrodes on thesymmetry of material 16 as drive electrodes, computing device 12 maycause a plurality of pairs of electrodes to be used as drive electrodes,as described above. In some examples, computing device 12 may causepairs of drive electrodes that are symmetric with reference to thesymmetry of material 16 or 32 to be used as drive electrodes, and foreach pair of drive electrodes, may cause measurement electrodes that aresymmetric to be used to measure voltages. For example, again withreference to FIG. 2, computing device 12 may cause electrodes E2 and E5to be used as a pair of drive electrodes. For E2 an E5 as the pair ofdrive electrodes, computing device 12 may cause one or more electrodesor pairs of electrodes to be used as the measurement electrode (or pairof measurement electrodes). For example, computing device 12 may causeE3 and E4 to be used as a pair of measurement electrodes, and,optionally, may cause at least some other (e.g., all other) adjacentpairs of electrodes (other than pairs of adjacent electrodes thatinclude electrodes E2 and E5) to be used as pairs of measurementelectrodes. As computing device 12 caused electrodes E2 and E5 to beused as a pair of drive electrodes, computing device 12 also may causeelectrodes E14 and E11 to be used as a pair of drive electrodes, sinceelectrodes E14 and E11 are symmetric to electrodes E2 and E5 withreference to plane of symmetry 34. Computing device 12 may causeelectrodes or pairs of electrodes that are symmetric to those used tomeasure voltages when electrodes E2 and E5 were used as the pair ofdrive electrodes to be used as measurement electrodes or pairs ofmeasurement electrodes.

In some examples, computing device 12 may repeat this technique for eachof a plurality of pairs of drive electrodes, each pair of driveelectrodes being symmetric to another pair of drive electrodes withreference to the symmetry of material 16 or 32 (e,g, plane of symmetry24 or 34). Computing device 12 then may determine whether material 16includes a crack or other defect by comparing respectivemeasured-voltages associated with respective measurement electrodes thatare substantially symmetrical with reference to the symmetry of material16 and for which respective pairs of drive electrodes that are symmetricto each other with reference to the symmetry of material 16 were used.

For each respective comparison, computing device 12 may compare a firstrespective measured voltage and a second respective measured voltage,and, in response to the first and second measured voltages beingsubstantially the same (e.g., within a threshold amount of each other)may determine that the comparison indicates that material 16 does notinclude a crack or other defect. On the other hand, in response to thefirst and second measured voltages not being substantially the same(e.g., different than each other by more than a threshold amount),computing device 12 may determine the comparison indicates that material16 includes a crack or other defect. The threshold amount may be thesame or slightly greater than the threshold amount used to determine theposition of electrodes IS. For example, the threshold amount may be 1%,5%, 10%, 20%, or the like. Computing device 12 may compare the first andsecond measured voltages by subtracting one of the first or secondmeasured voltages from the other of the first or second measuredvoltages, by taking a ratio of one of the first or second measuredvoltages to the other of the first or second measured voltages, or thelike, and then determining a percentage difference between the first orsecond measured voltages. Computing device 12 then may determine thatmaterial 16 includes a crack or other defect in response to at least oneof the comparisons indicating that material 16 includes a crack or otherdefect or in response to at least a threshold number of the comparisonsindicating that material 16 includes a crack or other defect.

In some examples, in addition to using the respective measured voltagesto determine whether material includes a crack or other defect (60),computing device 12 may utilize respective control voltages as describedabove with reference to FIG. 3.

FIG. 5 is another flow diagram illustrating another example techniquefor determining whether a material includes a crack or other defectbased on a comparison between at least a first measured voltageassociated with the material and a second measured voltage associatedwith the material. The technique of FIG. 5 will be described withconcurrent reference to system 10 of FIG. 1, but it will he understoodthat other systems that include more or fewer components than system 10may perform the technique of FIG. 5 (e.g., a system that includes onlycomputing device 12), and that system 10 may be used to perform othertechniques (e.g., the techniques of FIGS. 3 and 4, among othertechniques).

The technique of FIG. 5 includes selecting a group of electrodesincluding a pair of drive electrodes and a measurement electrode (72).Each respective group of electrodes may be geometrically configured toachieve measurement of a substantially similar voltage (e.g., the sameor nearly the same voltage) in the absence of a crack or other defect.Each respective group of electrodes may include a pair of driveelectrodes and one or two measurement electrodes. For example, a groupof electrodes may include a pair of drive electrodes separated by one ortwo measurement electrodes. Using electrodes 18 shown in FIG. 1, anexample of this configuration may include a pair of drive electrodesthat includes first electrode 18A and fourth electrode 18D, and a pairof measurement electrodes that includes second electrode 18B and thirdelectrode 18C. Another example of this configuration may include a pairof drive electrodes that includes first electrode 18A and thirdelectrode 18C, and a measurement electrode that includes secondelectrode 18B (to measure a single-ended voltage using second electrode18B and reference electrode 22). Other geometric configurations ofgroups of electrodes (e.g., other spacings between pairs of driveelectrodes and, optionally, pairs of measurement electrode) are alsopossible.

In some examples, each group of electrodes may not share any electrodeswith each other group of electrodes. In other examples, each group ofelectrodes may share one or more electrodes with another group ofelectrodes. For example, a first group of electrodes may include firstelectrode 18A and fourth electrode 18D as a pair of drive electrodes,and may include second electrode 8B and third electrode 18C as a pair ofdrive electrodes. A second group of electrodes may include secondelectrode 18B and fifth electrode 18E as a pair of drive electrodes, andthird electrode 18C and fourth electrode 18D as a pair of measurementelectrodes. In other words, each group of electrodes may include fourelectrodes, the two outer electrodes being drive electrodes and the twoinner electrodes being measurement electrodes. Each respective group ofelectrodes may be formed by four adjacent electrodes, and eachsubsequent group may be formed by moving one electrode to the right (orto the left). In some examples, the number of groups of electrodes mayequal the number of electrodes 18. In examples such as this, theplacement of each electrode of electrodes 18 may be so that the voltagemeasured using each respective group of electrodes is substantially thesame as the voltage measured using each other respective group ofelectrodes.

Computing device 12 may select the group of electrodes by causing switchnetwork 20 to electrically couple electrical signal source 14 to aselected pair of electrodes 18, which serves as a pair of driveelectrodes. Computing device 12 also may cause switch network 20 toelectrically couple computing device 12 to a selected measurementelectrode or pair of measurement electrodes. The selected pair ofmeasurement electrodes may be any two electrodes from electrodes 18,neither of which is being used as one of the electrodes in the pair ofdrive electrodes, or may be reference electrode 22 and any one ofelectrodes 18 that is not being used as one of the electrodes in thedrive pair of electrodes.

Computing device 12 then may cause electrical signal source 14 to applythe electrical signal to the first pair of drive electrodes electricallycoupled to material 16 (74), e.g., via switch network 20. The electricalsignal may include an AC signal or a DC signal, and may include acurrent signal or a voltage signal. In some examples, the type ofelectrical signal may depend on the composition of material 16. Forexample, a DC signal may be used to measure a voltage of an electricallyconductive or electrically semiconductive material, while an AC signalmay be used to measure a voltage of an electrically conductive material,an electrically semiconductive material, or a dielectric material.Computing device 12 also may control electrical signal source 14 togenerate the predetermined electrical signal with a selected amplitude,duration, frequency, and other signal characteristics.

Computing device 12 also may, while applying the electrical signal tothe pair of drive electrodes, determine a measured voltage using themeasurement electrode of the selected group (76). The technique of FIG.5 also includes determining, by computing device 12, whether there areadditional voltage measurements to be performed (78). Computing device12 may determine whether there are additional voltage measurements to beperformed (78) by determining whether there additional groups ofelectrodes to be selected. For example, computing device 12 may beconfigured to utilize each group of electrodes to determine a measuredvoltage.

Upon determining that there is an additional voltage measurement to beperformed (the “YES” branch of decision block 78), computing device 12may select a new group of electrodes by causing switch network 20 toelectrically couple the selected pair of drive electrodes to electricalsignal source 14 and causing switch network 20 to electrically couplethe selected measurement electrode to computing device 12. Computingdevice 12 then may cause electrical signal source 14 to apply theelectrical signal to the new selected pair of drive electrodes (74),and, while electrical signal source 14 is applying the electrical signalto the selected pair of drive electrodes (74), may determine arespective measured voltage using the selected measurement electrode(76). Again, computing device 12 may determine whether there is areadditional measurements to be performed (78). In response to determiningthat there is an additional voltage measurement to be performed (the“YES” branch of decision block 78), computing device 12 may select a newgroup of electrodes by causing switch network 20 to electrically couplethe selected pair of drive electrodes to electrical signal source 14 andcausing switch network 20 to electrically couple the selectedmeasurement electrode to computing device 12. Computing device 12 thenmay cause electrical signal source 14 to apply the electrical signal tothe new selected pair of drive electrodes (74), and, while electricalsignal source 14 is applying the electrical signal to the selected pairof drive electrodes (74), may determine a respective measured voltageusing the selected measurement electrode (76). Computing device 12 mayrepeat this algorithm until determining that there are no additionalmeasurements to be performed (the “NO” branch of decision block 78).

Computing device 12 then may determine whether material 16 includes acrack or other defect based on the respective measured voltages (80). Asdescribed above, for each group, the measured voltage in the absence ofa crack or other defect is substantially the same. As such, computingdevice 12 may compare any measured voltage to any other measured voltage(or multiple other measured voltages) to determine if the measuredvoltage indicates that material 16 includes a crack or other defect. Forexample, computing device 12 may compare each measured voltage to eachother measured voltage, and determine if each respective comparisonindicates that material 16 includes a crack or other defect.

In response to a first respective measured voltage being substantiallythe same as a second respective measured voltage (e.g., within athreshold amount of each other), computing device 12 may determine thatthe comparison indicates that material 16 does not include a crack orother defect. On the other hand, a first respective measured voltage notbeing substantially the same as a second respective measured voltage(e.g., different than each other by more than a threshold amount),computing device 12 may determine the comparison indicates that material16 includes a crack or other defect. The threshold amount may be thesame or slightly greater than the threshold amount used to determine theposition of electrodes 18. For example, the threshold amount may be 1%,5%, 10%, 20%, or the like. Computing device 12 may compare therespective measured voltages by subtracting one of the respectivemeasured voltages from the other of the respective measured voltages, bytaking a ratio of one of the respective measured. voltages and the otherof the respective measured voltages, or the like, and then determining apercentage difference between the respective measured voltages.Computing device 12 then may determine that material 16 includes a crackor other defect in response to at least one of the comparisonsindicating that material 16 includes a crack or other defect or inresponse to at least a threshold number of the comparisons indicatingthat material 16 includes a crack or other defect.

In some examples, in addition to using the respective measured voltagesto determine whether material includes a crack or other defect (80),computing device 12 may utilize respective control voltages as describedabove with reference to FIG. 3.

In any of the techniques described herein, computing device 12 mayoutput a representation of the determination of whether material 16includes a crack or other defect. In some examples, the representationmay include a simplified output, such as an indication of “Yes” or “No,”“Crack” or “No Crack,” “Damaged” or “Intact,” or the like. Therepresentation may be textual, icon-based, color-based, or the like. Forexample, the representation may include a green light to represent thatmaterial 16 is still intact or a red light to represent that material 16is damages or includes a crack or other defect.

In this way, utilizing comparisons between multiple voltage measurementsfrom a material may allow determination of whether a material includes acrack or other defect without previous measurement of control voltages,which may simplify determination of whether the material includes thecrack or other defect. Further, as the multiple voltage measurements areperformed at substantially the same time (e.g., as part of a single setof measurements), the material may be expected to be at substantiallythe same temperature (e.g., the same temperature or nearly the sametemperature). Thus, temperature may be less of a factor in thecomparisons. This may be important for some materials, such assemiconductors, whose conductivity changes significantly as a functionof temperature.

The techniques described in this disclosure may be implemented, at leastin part, in hardware, software, firmware, or any combination thereof.For example, various aspects of the described techniques may beimplemented within one or more processors, including one or moremicroprocessors, digital signal processors (DSPs), application specificintegrated circuits (ASICs), field programmable gate arrays (FPGAs), orany other equivalent integrated or discrete logic circuitry, as well asany combinations of such components. The term “processor” or “processingcircuitry” may generally refer to any of the foregoing logic circuitry,alone or in combination with other logic circuitry, or any otherequivalent circuitry. A control unit including hardware may also performone or more of the techniques of this disclosure.

Such hardware, software, and firmware may be implemented within the samedevice or within separate devices to support the various techniquesdescribed in this disclosure. In addition, any of the described, units,modules or components may be implemented together or separately asdiscrete but interoperable logic devices. Depiction of differentfeatures as modules or units is intended to highlight differentfunctional aspects and does not necessarily imply that such modules orunits must be realized by separate hardware, firmware, or softwarecomponents. Rather, functionality associated with one or more modules orunits inlay be performed by separate hardware, firmware, or softwarecomponents, or integrated within common or separate hardware, firmware,or software components.

The techniques described in this disclosure may also be embodied orencoded in an article of manufacture including a computer-readablestorage medium encoded with instructions. Instructions embedded orencoded in an article of manufacture including a computer-readablestorage medium encoded, may cause one or more programmable processors,or other processors, to implement one or more of the techniquesdescribed herein, such as when instructions included or encoded in thecomputer-readable storage medium are executed by the one or moreprocessors. Computer readable storage media may include random accessmemory (RAM), read only memory (ROM), programmable read only memory(PROM), erasable programmable read only memory (EPROM), electronicallyerasable programmable read only memory (EEPROM), flash memory, a harddisk, a compact disc ROM (CD-ROM), a floppy disk, a cassette, magneticmedia, optical media, or other computer readable media. In someexamples, an article of manufacture may include one or morecomputer-readable storage media.

In some examples, a computer-readable storage medium may include anon-transitory medium. The term “non-transitory” may indicate that thestorage medium is not embodied in a carrier wave or a propagated signal.In certain examples, a non-transitory storage medium may store data thatcan, over time, change (e.g., in RAM or cache).

Clause 1: A method for detecting a crack or defect in a material, themethod comprising: applying a first electrical signal to a first pair ofdrive electrodes, wherein the, first pair of drive electrodes isselected from a set of N electrodes electrically coupled to thematerial; while applying the first electrical signal to the first pairof drive electrodes, determining a first measured voltage using a firstmeasurement electrode, wherein the first measurement electrode is fromthe set of N electrodes; applying a second electrical signal to a secondpair of drive electrodes, wherein the second pair of drive electrodes isselected from the set of N electrodes; while applying the secondelectrical signal to the second pair of drive electrodes, determining asecond measured voltage using a second, different measurement electrode,wherein the second, different measurement electrode is from the set of Nelectrodes; and determining whether the material includes a crack orother defect based on a comparison between the first measured voltageand the second measured voltage.

Clause 2: The method of clause 1, wherein the first electrical signal issubstantially the same as the second electrical signal.

Clause 3: The method of claim 1 or 2, wherein: the first pair of driveelectrodes and the second pair of drive electrodes is the same pair ofdrive electrodes; the respective electrodes of the pair of driveelectrodes is disposed on a symmetry of the material; and the firstmeasurement electrode is substantially symmetrical to the second,different measurement electrode with reference to the symmetry of thematerial.

Clause 4: The method of clause 3, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach electrode of the set of N electrodes to another electrode of theset of N electrodes.

Clause 5: The method of clause 1 or 2, wherein: the first pair of driveelectrodes is different from the second pair of drive electrodes; thefirst pair of drive electrodes is substantially symmetrical to thesecond pair of drive electrodes with reference to the symmetry of thematerial; and the first measurement electrode is substantiallysymmetrical to the second, different measurement electrode withreference to the symmetry: of the material.

Clause 6: The method of clause 5, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to symmetry the mapseach electrode of the set of N electrodes to another electrode of set ofN electrodes.

Clause 7: The method of any one of clauses 1 to 6, wherein the geometricconfiguration of the first pair of drive electrodes and the firstmeasurement electrode, and the geometric configuration of the secondpair of drive electrodes and the second, different measurement electrodeare selected so that, in the absence of a crack or other defect, thefirst measured voltage is substantially the same as the second measuredvoltage.

Clause 8: The method of clause 7, wherein determining whether thematerial includes the crack or other defect based on the comparisonbetween the first measured voltage and the second measured voltagecomprises determining that the material includes the crack or otherdefect in response to the first measured voltage and the second measuredvoltage being different by more than a threshold amount.

Clause 9: The method of any one of clauses 1 to 8, wherein theelectrical signal is a voltage signal or a current signal.

Clause 10: The method of any one of clauses 1 to 9, further comprising,before determining whether the material includes the crack or otherdefect based on the comparison between the first measured voltage andthe second measured voltage: determining a first adjusted measuredvoltage based on the first measured voltage and a first control voltageassociated with the first measurement electrode, determining a secondadjusted measured voltage based on the second measured voltage and asecond control voltage associated with the second, different measurementelectrode; wherein determining whether the material includes the crackor other defect based on the comparison between the first measuredvoltage and the second measured voltage comprises determining whetherthe material includes the crack or other defect based on a comparisonbetween the first adjusted measured voltage and the second adjustedmeasured voltage.

Clause 11: The method of any one of clauses 1 to 10, wherein: aplurality of electrodes are distributed across a surface area of thematerial; and the plurality of electrodes include the first pair ofdrive electrodes, the second pair of drive electrodes, the firstmeasurement electrode, and the second, different measurement electrode.

Clause 12: The method of any one of clauses 1 to 10, wherein: aplurality of electrodes are distributed around a perimeter of thematerial; and the plurality of electrodes include the first pair ofdrive electrodes, the second pair of drive electrodes, the firstmeasurement electrode, and the second measurement electrode.

Clause 13: The method of any one of claims 1 to 12, wherein: determiningthe first measured voltage using the first measurement electrodecomprises determining the first measured voltage between a first pair ofmeasurement electrodes; the first pair of measurement electrodes isselected from the set of N electrodes; determining the second measuredvoltage using the second, different measurement electrode comprisesdetermining the second measured voltage between a second, different pairof measurement electrodes; and the second, different pair of measurementelectrodes is from the set of N electrodes.

Clause 14: A method for detecting a crack or defect in a material, themethod comprising: for each respective pair of drive electrodes of atleast one pair of drive electrodes electrically coupled to the material,applying an electrical signal to the respective pair of driveelectrodes; for each respective pair of drive electrodes, determining arespective measured voltage using a respective measurement electrode ofa plurality of measurement electrodes while applying the electricalsignal to the respective pair of drive electrodes, wherein eachrespective measurement electrode is substantially symmetrical to anothermeasurement electrode with reference to a symmetry of the material, andwherein the plurality of measurement electrodes are electrically coupledto the material; and determining whether the material includes a crackor other defect based on comparisons between the respective measuredvoltages associated with respective measurement electrodes that aresubstantially symmetrical with reference to the symmetry of thematerial.

Clause 15: The method of clause 14, wherein: the at least one pair ofdrive electrodes is a single pair of drive electrodes; the respectiveelectrodes of the single pair of drive electrodes are disposed on thesymmetry of the material.

Clause 16: The method of clause 15, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach measurement electrode of the plurality of measurement electrodes toanother measurement electrode of the plurality of measurementelectrodes.

Clause 17: The method of clause 14, wherein: the at least one pair ofdrive electrodes includes a plurality of pairs of drive electrodes; andeach respective pair of drive electrodes is substantially symmetrical toanother pair of drive electrodes with reference to a symmetry of thematerial.

Clause 18: The method of clause 17, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach respective pair of drive electrodes of the plurality of pairs ofdrive electrodes to another respective pair of drive electrodes of theplurality of pairs of drive electrodes.

Clause 19: The method of any one of clauses 14 to 18, wherein theelectrical signal is a voltage signal or a current signal.

Clause 20: The method of any one of clauses 14 to 19, whereindetermining whether the material includes a crack or other defect basedon comparisons between the respective measured voltages associated withrespective measurement electrodes that are substantially symmetricalwith reference to the symmetry of the material comprises determiningthat the material includes the crack or other defect in response to arespective measured voltage associated with a first measurementelectrode being different by more than a threshold amount from arespective measured voltage associated with a second measurementelectrode that is substantially symmetrical to the first measurementelectrode.

Clause 21: The method of any one of clauses 14 to 20, furthercomprising, before determining whether the material includes a crack orother defect based on comparisons between the respective measuredvoltages associated with respective measurement electrodes that aresubstantially symmetrical with reference to the symmetry of thematerial: for each respective measured voltage, determining respectiveadjusted measured voltage based on the respective measured voltage and arespective reference voltage associated with the respective measurementelectrode; and wherein determining whether the material includes a crackor other defect based on comparisons between the respective measuredvoltages associated with respective measurement electrodes that aresubstantially symmetrical with reference to the symmetry of the materialcomprises determining whether the material includes the crack or otherdefect based on comparisons between the respective adjusted measuredvoltages associated with respective measurement electrodes that aresubstantially symmetrical with reference to the symmetry of thematerial.

Clause 22: The method of any one of clauses 14 to 21, wherein aplurality of electrodes are distributed across a surface area of thematerial, and wherein the plurality of electrodes include the at leastone pair of drive electrodes and the plurality of measurementelectrodes.

Clause 23: The method of any one of clauses 14 to 21, wherein aplurality of electrodes are distributed around a perimeter of thematerial, and wherein the plurality of electrodes include the at leastone pair of drive electrodes and the plurality of measurementelectrodes.

Clause 24: The method of any one of clauses 14 to 23, whereindetermining the respective measured voltage using the respectivemeasurement electrode of the plurality of measurement electrodes whileapplying the electrical signal to the respective pair of driveelectrodes comprises determining a respective measured voltage between arespective pair of measurement electrodes of the plurality ofmeasurement electrodes while applying the electrical signal to therespective pair of drive electrodes.

Clause 25: A method for detecting a crack or defect in a material, themethod comprising: for each respective pair of drive electrodes of aplurality of pairs of drive electrodes electrically coupled to thematerial, applying a respective electrical signal to the respective pairof drive electrodes; for each respective pair of drive electrodes,determining a respective measured voltage using a respective measurementelectrode of a plurality of measurement electrodes while applying theelectrical signal to the respective pair of drive electrodes, whereinthe geometric configuration of each respective combination of arespective pair of drive electrodes and a respective measurementelectrode is selected so that, in the absence of a crack, eachrespective measured voltage is substantially the same as at least oneother respective measured voltage; and determining whether the materialincludes a crack or other defect based on comparisons between therespective measured voltages.

Clause 26: The method of clause 25, wherein the geometric configurationof each respective combination of a respective pair of drive electrodesand a respective measurement electrode is selected so that, in theabsence of a crack, each respective measured voltage is substantiallythe same as each other respective measured voltage.

Clause 27: The method of clause 25 or 26, wherein determining therespective measured voltage using the respective measurement electrodeof the plurality of measurement electrodes while applying the electricalsignal to the respective pair of drive electrodes comprises determininga respective measured voltage between a respective pair of measurementelectrodes of the plurality of measurement electrodes while applying theelectrical signal to the respective pair of drive electrodes, whereinthe geometric configuration of each respective pair of drive electrodesand the respective pair of measurement electrodes is selected so that,in the absence of a crack, each respective measured voltage issubstantially the same as all other respective measured voltages.

Clause 28: The method of any one of clauses 25 to 27, furthercomprising, before determining whether the material includes the crackor other defect based on comparisons between the respective measuredvoltages: for each respective measured voltage, determining a respectiveadjusted measured voltage based on the respective measured voltage and arespective control voltage associated with the respective measurementelectrode; wherein determining whether the material includes the crackor other defect based on comparisons between the respective measuredvoltages comprises determining whether the material includes a crack orother defect based on comparisons between the respective adjustedmeasured voltages.

Clause 29: The method of any one of clauses 25 to 28, wherein theelectrical signal is a voltage signal or a current signal.

Clause 30: The method of any one of clauses 25 to 29, wherein eachrespective applied electrical signal is substantially the same.

Clause 31: The method of any one of clauses 25 to 30, whereindetermining whether the material includes the crack or other defectbased on comparisons between the respective measured voltages comprisesdetermining that the material includes the crack or other defect inresponse to a first respective voltage being different than at least oneother respective voltage by more than a threshold amount.

Clause 32: The method of any one of clauses 25 to 31, wherein aplurality of electrodes are distributed across a surface area of thematerial, and wherein the plurality of electrodes include the pluralityof pairs of drive electrodes and the plurality of measurementelectrodes.

Clause 33: The method of any one of clauses 25 to 31, wherein aplurality of electrodes are distributed around a perimeter of thematerial, and wherein the plurality of electrodes include the pluralityof pairs of drive electrodes and the plurality of measurementelectrodes.

Clause 34: A system comprising: a set of N electrodes electricallycoupled to a material; an electrical signal source; and a computingdevice configured to: cause the electrical signal source to apply afirst electrical signal to a first pair of drive electrodes, wherein thefirst pair of drive electrodes is selected from the set of N electrodes;while the electrical signal source is applying the first electricalsignal to the first pair of drive electrodes, determine a first measuredvoltage using a first measurement electrode, wherein the firstmeasurement electrode is from the set of N electrodes; cause theelectrical signal source to apply a second electrical signal to a secondpair of drive electrodes, wherein the second pair of drive electrodes isselected from the set of N electrodes; while the electrical signalsource is applying the second electrical signal to the second pair ofdrive electrodes, determine a second measured voltage using a second,different measurement electrode, wherein the second, differentmeasurement electrode is from the set of N electrodes; and determinewhether the material includes a crack or other defect based on acomparison between the first measured voltage and the second measuredvoltage.

Clause 35: The system of clause 34, wherein the first electrical signalis substantially the same as the second electrical signal.

Clause 36: The system of clause 34 or 35, wherein: the first pair ofdrive electrodes and the second pair of drive electrodes is the samepair of drive electrodes; the respective electrodes of the pair of driveelectrodes is disposed on a symmetry of the material; and the firstmeasurement electrode is substantially symmetrical to the second,different measurement electrode with reference to the symmetry of thematerial.

Clause 37: The system of clause 36, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach electrode of the set of N electrodes to another electrode of theset of N electrodes.

Clause 38: The system of clause 34 or 35, wherein: the first pair ofdrive electrodes is different from the second pair of drive electrodes;the first pair of drive electrodes is substantially symmetrical to thesecond pair of drive electrodes with reference to the symmetry of thematerial; and the first measurement electrode is substantiallysymmetrical to the second, different measurement electrode withreference to the symmetry of the material.

Clause 39: The system of clause 38, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach electrode of the set of N electrodes to another electrode of set ofN electrodes.

Clause 40: The system of any one of clauses 34 to 39, wherein thegeometric configuration of the first pair of drive electrodes and thefirst measurement electrode, and the geometric configuration of thesecond pair of drive electrodes and the second, different measurementelectrode are selected so that, in the absence of a crack, the firstmeasured voltage is substantially the same as the second measuredvoltage.

Clause 41: The system of clause 40, wherein the computing device isconfigured to determine whether the material includes the crack or otherdefect based on the comparison between the first measured voltage andthe second measured voltage by at least determining that the materialincludes the crack or other defect in response to the first measuredvoltage and the second measured voltage being different by more than athreshold amount.

Clause 42: The system of any one of clauses 34 to 41, wherein theelectrical signal is a voltage signal or a current signal.

Clause 43: The system of any one of clauses 34 to 42, wherein thecomputing device is further configured to, before determining whetherthe material includes the crack or other defect based on the comparisonbetween the first measured voltage and the second measured voltage:determine a first adjusted measured voltage based on the first measuredvoltage and a first control voltage associated with the firstmeasurement electrode; and determine a second adjusted measured voltagebased on the second measured voltage and a second control voltageassociated with the second, different measurement electrode; and whereinthe computing device is configured to determine whether the materialincludes the crack or other defect based on the comparison between thefirst measured voltage and the second measured voltage by at leastdetermining whether the material includes the crack or other defectbased on a comparison between the first adjusted measured voltage andthe second adjusted measured voltage.

Clause 44: The system of any one of clauses 34 to 43, wherein the set ofN electrodes is distributed across a surface area of the material.

Clause 45: The system of any one of clauses 34 to 43, wherein the set ofN electrodes is distributed around a perimeter of the material.

Clause 46: The system of any one of clauses 34 to 45, wherein: thecomputing device is configured to determine the first measured voltagebetween a first pair of measurement electrodes and determine the secondmeasured voltage between a second, different pair of measurementelectrodes; and the first pair of measurement electrodes and the second,different pair of measurement electrodes are selected from the set of Nelectrodes.

Clause 47: A system comprising: a set of N electrodes electricallycoupled to a material; an electrical signal source; and a computingdevice configured to: for each respective pair of drive electrodes of atleast one pair of drive electrodes, cause the electrical signal sourceto apply an electrical signal to the respective pair of driveelectrodes, wherein the at least one pair of drive electrodes is fromthe set of N electrodes; for each respective pair of drive electrodes,determine a respective measured voltage using a respective measurementelectrode of a plurality of measurement electrodes while the electricalsignal source is applying the electrical signal to the respective pairof drive electrodes, wherein each respective measurement electrode issubstantially symmetrical to another measurement electrode withreference to the symmetry of the material, and wherein the plurality ofmeasurement electrodes are from the set of N electrodes; and determinewhether the material includes a crack or other defect based oncomparisons between the respective measured voltages associated withrespective measurement electrodes that are substantially symmetricalwith reference to the symmetry of the material.

Clause 48: The system of clause 47, wherein: the at least one pair ofdrive electrodes is a single pair of drive electrodes; the respectiveelectrodes of the single pair of drive electrodes are disposed on thesymmetry of the material.

Clause 49: The system of clause 48, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach measurement electrode of the plurality of measurement electrodes toanother measurement electrode of the plurality of measurementelectrodes.

Clause 50: The system of clause 47, wherein: the at least one pair ofdrive electrodes includes a plurality of pairs of drive electrode pairs;each respective pair of drive electrodes is substantially symmetrical toanother pair of drive electrodes with reference to a symmetry of thematerial.

Clause 51: The system of clause 50, wherein the symmetry of the materialis a point, a line, a plane, a curve, or a manifold, and wherein asingle mathematical operation made with reference to the symmetry mapseach respective pair of drive electrodes of the plurality of pairs ofdrive electrodes to another respective pair of drive electrodes of theplurality of pairs of drive electrodes.

Clause 52: The system of any one of clauses 47 to 51, wherein theelectrical signal is a voltage signal or a current signal.

Clause 53: The system of any one of clauses 4 to 52, wherein thecomputing device is configured to determine whether the materialincludes the crack or other defect by at least determining that thematerial includes the crack or other defect in response to a respectivemeasured voltage associated with a first measurement electrode beingdifferent by more than a threshold amount from a respective measuredvoltage associated with a second measurement electrode that issubstantially symmetrical to the first measurement electrode.

Clause 54: The system of any one of clauses 47 to 53, wherein: thecomputing device is further configured to, before determining whetherthe material includes a crack or other defect, for each respectivemeasured voltage, determine respective adjusted measured voltage basedon the respective measured voltage and a respective reference voltageassociated with the respective measurement electrode; and the computingdevice is configured to determine whether the material includes a crackor other defect by at least determining whether the material includesthe crack or other defect based on comparisons between the respectiveadjusted measured voltages associated with respective measurementelectrodes that are substantially symmetrical with reference to thesymmetry of the material,

Clause 55: The system of any one of clauses 47 to 54, wherein the set ofN electrodes is distributed across a surface area of the material.

Clause 56: The system of any one of clauses 47 to 54, wherein the set ofN electrodes is distributed around a perimeter of the material.

Clause 57: The system of any one of clauses 47 to 56, wherein thecomputing device is configured to determine a respective measuredvoltage between a respective pair of measurement electrodes of theplurality of measurement electrodes while applying the electrical signalto the respective pair of drive electrodes.

Clause 58: A system comprising: a set of N electrodes electricallycoupled to a material; an electrical signal source; and a computingdevice configured to: for each respective pair of drive electrodes of aplurality of pairs of drive electrodes electrically coupled to thematerial, cause the electrical signal source to apply a respectiveelectrical signal to the respective pair of drive electrodes, whereinthe plurality of pairs of drive electrodes are from the set of Nelectrodes; for each respective pair of drive electrodes, determine arespective measured voltage using a respective measurement electrode ofa plurality of measurement electrodes while the electrical signal sourceis applying the electrical signal to the respective pair of driveelectrodes, wherein a geometric configuration of each respectivecombination of a pair of drive electrodes and a respective measurementelectrode is selected so that, in the absence of a crack, eachrespective measured voltage is substantially the same as at least oneother respective measured voltage; and determine whether the materialincludes a crack or other defect based on comparisons between therespective measured voltages.

Clause 59: The system of clause 58, wherein the geometric configurationof each respective combination of a pair of drive electrodes and arespective measurement electrode is selected so that, in the absence ofa crack, each respective measured voltage is substantially the same aseach other respective measured voltage.

Clause 60: The system of claim 58 or 59, wherein the computing device isconfigured to determine a respective measured voltage between arespective pair of measurement electrodes of the plurality ofmeasurement electrodes while applying the electrical signal to therespective pair of drive electrodes, wherein the geometric configurationof each respective pair of drive electrodes and the respective pair ofmeasurement electrodes is selected so that, in the absence of a crack,each respective measured voltage is substantially the same as all otherrespective measured voltages.

Clause 61: The system of any one of clauses 58 to 60, wherein: thecomputing device is further configured to, before determining whetherthe material includes the crack or other defect based on comparisonsbetween the respective measured voltages, for each respective measuredvoltage, determining a respective adjusted measured voltage based on therespective measured voltage and a respective control voltage associatedwith the respective measurement electrode; and the computing device isconfigured to determine whether the material includes the crack or otherdefect by at least determining whether the material includes a crack orother defect based on comparisons between the respective adjustedmeasured voltages.

Clause 62: The system of any one of clauses 58 to 61, wherein theelectrical signal is a voltage signal or a current signal.

Clause 63: The system of any one of clauses 58 to 62, wherein eachrespective applied electrical signal is substantially the same.

Clause 64: The system of any one of clauses 58 to 63, wherein thecomputing device is configured to determine whether the materialincludes the crack or other defect by at least determining that thematerial includes the crack or other defect in response to a firstrespective voltage being different than at least one other respectivevoltage by more than a threshold amount.

Clause 65: The system of any one of clauses 58 to 64, wherein the set ofN electrodes is distributed across a surface area of the material.

Clause 66: The system of any one of clauses 58 to 64, wherein the set ofN electrodes is distributed around a perimeter of the material.

EXAMPLE

A 2D model simulation was used to place electrodes. The initial CADdescribing the material was imported and using a combination of meshingtools (Gmsh, Netgen) and Electrical Impedance Tomography and DiffuseOptical Tomography Reconstruction Software (EIDORS) functions, the meshshown in FIG. 6 was created and used in simulations. EIDORS is availableat eidors3d.sourceforge.net. The simulations for positioning theelectrodes included the following steps:

1. Identify a plane of symmetry.

2. Place two electrodes on this plane of symmetry.

3. Place an equal number of electrodes on either side of the plane ofsymmetry, such that the additional electrodes result in symmetry of thecombined system.

4. For each integer 1:16. simulate an applied current to a pair of driveelectrodes X and X+3, determine a simulated measured voltage at a pairof measurement electrodes X+1 and X+2. This simulation was performed inMATLAB® using the algorithm fwd_solve in the package EIDORS was used tosolve the reconstruction problem. MATLAB® is available from MathWorks®,Inc., Natick, Mass., United States.

5. Determine a minimum measured voltage for the 16 measured voltages,along with the electrode numbers of the pair of measurement electrodesassociated with the minimum voltage.

6. Determine the measured voltages for the pairs of measurementelectrodes on either side of the pair of measurement electrodesassociated with the minimum measured voltage.

7. Determine which voltage between the measured voltages on either sideof the minimum measured voltage is larger.

8. Identify the common electrode from the pair of electrodes associatedwith the minimum measured voltage and the pair of electrodes associatedwith the larger measured voltage between the pairs of measurementelectrodes on either side of the pair of measurement electrodesassociated with the minimum measured voltage.

9. Move the common electrode away from the other electrode in the pairof electrodes associated with the minimum value by a predetermineddistance.

10. Move the electrode that is symmetric to the electrode that is movedin step 9 to maintain symmetry of the electrodes.

11. Iterate steps 4 to 10 until the measured voltages fall within aspecified tolerance.

FIG. 6 is a diagram illustrating an example finite element model of amaterial that includes electrodes positioned on the material. Theelectrode positions determined by the simulation were (in units of mm):

Electrode X Z 0 0 135 1 0 81.57041 2 54.21065 0 3 113.2 0 4 159.6842 0 5211.5059 0 6 275.1349 19.54934 7 325.3673 58.61904 8 340 135 9 325.3673211.381 10 275.1349 250.4507 11 211.5059 270 12 159.6842 270 13 113.2270 14 52.21065 270 15 0 188.4296

Various examples have been described. These and other examples arewithin the scope of the following claims.

1. A method for detecting a crack or defect in a material, the methodcomprising: applying a first electrical signal to a first pair of driveelectrodes, wherein the first pair of drive electrodes is selected froma set of N electrodes electrically coupled to the material; whileapplying the first electrical signal to the first pair of driveelectrodes, determining a first measured voltage using a firstmeasurement electrode, wherein the first measurement electrode is fromthe set of N electrodes; applying a second electrical signal to a secondpair of drive electrodes, wherein the second pair of drive electrodes isselected from the set of N electrodes; while applying the secondelectrical signal to the second pair of drive electrodes, determining asecond measured voltage using a second, different measurement electrode,wherein the second, different measurement electrode is from the set of Nelectrodes; and determining whether the material includes a crack orother defect based on a comparison between the first measured voltageand the second measured voltage; wherein the method further comprises,before determining whether the material includes the crack or otherdefect based on the comparison between the first measured voltage andthe second measured voltage: determining a first adjusted measuredvoltage based on the first measured voltage and a first control voltageassociated with the first measurement electrode; determining a secondadjusted measured voltage based on the second measured voltage and asecond control voltage associated with the second, different measurementelectrode; wherein determining whether the material includes the crackor other defect based on the comparison between the first measuredvoltage and the second measured voltage comprises determining whetherthe material includes the crack or other defect based on a comparisonbetween the first adjusted measured voltage and the second adjustedmeasured voltage. 2-13. (canceled)
 14. A method for detecting a crack ordefect in a material, the method comprising: for each respective pair ofdrive electrodes of at least one pair of drive electrodes electricallycoupled to the material, applying an electrical signal to the respectivepair of drive electrodes; for each respective pair of drive electrodes,determining a respective measured voltage using a respective measurementelectrode of a plurality of measurement electrodes while applying theelectrical signal to the respective pair of drive electrodes, whereineach respective measurement electrode is substantially symmetrical toanother measurement electrode with reference to a symmetry of thematerial, and wherein the plurality of measurement electrodes areelectrically coupled to the material; and determining whether thematerial includes a crack or other defect based on comparisons betweenthe respective measured voltages associated with respective measurementelectrodes that are substantially symmetrical with reference to thesymmetry of the material.
 15. The method of claim 14, wherein: the atleast one pair of drive electrodes is a single pair of drive electrodes;the respective electrodes of the single pair of drive electrodes aredisposed on the symmetry of the material.
 16. The method of claim 15,wherein the symmetry of the material is a point, a line, a plane, acurve, or a manifold, and wherein a single mathematical operation madewith reference to the symmetry maps each measurement electrode of theplurality of measurement electrodes to another measurement electrode ofthe plurality of measurement electrodes.
 17. The method of claim 14,wherein: the at least one pair of drive electrodes includes a pluralityof pairs of drive electrodes; and each respective pair of driveelectrodes is substantially symmetrical to another pair of driveelectrodes with reference to a symmetry of the material.
 18. The methodof claim 17, wherein the symmetry of the material is a point, a line, aplane, a curve, or a manifold, and wherein a single mathematicaloperation made with reference to the symmetry maps each respective pairof drive electrodes of the plurality of pairs of drive electrodes toanother respective pair of drive electrodes of the plurality of pairs ofdrive electrodes.
 19. (canceled)
 20. The method of claim 14, whereindetermining whether the material includes a crack or other defect basedon comparisons between the respective measured voltages associated withrespective measurement electrodes that are substantially symmetricalwith reference to the symmetry of the material comprises determiningthat the material includes the crack or other defect in response to arespective measured voltage associated with a first measurementelectrode being different by more than a threshold amount from arespective measured voltage associated with a second measurementelectrode that is substantially symmetrical to the first measurementelectrode.
 21. The method of claim 14, further comprising, beforedetermining whether the material includes a crack or other defect basedon comparisons between the respective measured voltages associated withrespective measurement electrodes that are substantially symmetricalwith reference to the symmetry of the material: for each respectivemeasured voltage, determining respective adjusted measured voltage basedon the respective measured voltage and a respective reference voltageassociated with the respective measurement electrode; and whereindetermining whether the material includes a crack or other defect basedon comparisons between the respective measured voltages associated withrespective measurement electrodes that are substantially symmetricalwith reference to the symmetry of the material comprises determiningwhether the material includes the crack or other defect based oncomparisons between the respective adjusted measured voltages associatedwith respective measurement electrodes that are substantiallysymmetrical with reference to the symmetry of the material. 22.(canceled)
 23. The method of claim 14, wherein a plurality of electrodesare distributed around a perimeter of the material, and wherein theplurality of electrodes include the at least one pair of driveelectrodes and the plurality of measurement electrodes.
 24. The methodof claim 14, wherein determining the respective measured voltage usingthe respective measurement electrode of the plurality of measurementelectrodes while applying the electrical signal to the respective pairof drive electrodes comprises determining a respective measured voltagebetween a respective pair of measurement electrodes of the plurality ofmeasurement electrodes while applying the electrical signal to therespective pair of drive electrodes. 25-46. (canceled)
 47. A systemcomprising: a set of N electrodes electrically coupled to a material; anelectrical signal source; and a computing device configured to: for eachrespective pair of drive electrodes of at least one pair of driveelectrodes, cause the electrical signal source to apply an electricalsignal to the respective pair of drive electrodes, wherein the at leastone pair of drive electrodes is from the set of N electrodes; for eachrespective pair of drive electrodes, determine a respective measuredvoltage using a respective measurement electrode of a plurality ofmeasurement electrodes while the electrical signal source is applyingthe electrical signal to the respective pair of drive electrodes,wherein each respective measurement electrode is substantiallysymmetrical to another measurement electrode with reference to thesymmetry of the material, and wherein the plurality of measurementelectrodes are from the set of N electrodes; and determine whether thematerial includes a crack or other defect based on comparisons betweenthe respective measured voltages associated with respective measurementelectrodes that are substantially symmetrical with reference to thesymmetry of the material.
 48. The system of claim 47, wherein: the atleast one pair of drive electrodes is a single pair of drive electrodes;the respective electrodes of the single pair of drive electrodes aredisposed on the symmetry of the material.
 49. (canceled)
 50. The systemof claim 47, wherein: the at least one pair of drive electrodes includesa plurality of pairs of drive electrode pairs; each respective pair ofdrive electrodes is substantially symmetrical to another pair of driveelectrodes with reference to a symmetry of the material.
 51. The systemof claim 50, wherein the symmetry of the material is a point, a line, aplane, a curve, or a manifold, and wherein a single mathematicaloperation made with reference to the symmetry maps each respective pairof drive electrodes of the plurality of pairs of drive electrodes toanother respective pair of drive electrodes of the plurality of pairs ofdrive electrodes.
 52. (canceled)
 53. The system of claim 47, wherein thecomputing device is configured to determine whether the materialincludes the crack or other defect by at least determining that thematerial includes the crack or other defect in response to a respectivemeasured voltage associated with a first measurement electrode beingdifferent by more than a threshold amount from a respective measuredvoltage associated with a second measurement electrode that issubstantially symmetrical to the first measurement electrode.
 54. Thesystem of claim 47, wherein: the computing device is further configuredto, before determining whether the material includes a crack or otherdefect, for each respective measured voltage, determine respectiveadjusted measured voltage based on the respective measured voltage and arespective reference voltage associated with the respective measurementelectrode; and the computing device is configured to determine whetherthe material includes a crack or other defect by at least determiningwhether the material includes the crack or other defect based oncomparisons between the respective adjusted measured voltages associatedwith respective measurement electrodes that are substantiallysymmetrical with reference to the symmetry of the material.
 55. Thesystem of claim 47, wherein the set of N electrodes is distributedacross a surface area of the material.
 56. The system of claim 47,wherein the set of N electrodes is distributed around a perimeter of thematerial.
 57. The system of claim 47, wherein the computing device isconfigured to determine a respective measured voltage between arespective pair of measurement electrodes of the plurality ofmeasurement electrodes while applying the electrical signal to therespective pair of drive electrodes.
 58. A system comprising: a set of Nelectrodes electrically coupled to a material; an electrical signalsource; and a computing device configured to: for each respective pairof drive electrodes of a plurality of pairs of drive electrodeselectrically coupled to the material, cause the electrical signal sourceto apply a respective electrical signal to the respective pair of driveelectrodes, wherein the plurality of pairs of drive electrodes are fromthe set of N electrodes; for each respective pair of drive electrodes,determine a respective measured voltage using a respective measurementelectrode of a plurality of measurement electrodes while the electricalsignal source is applying the electrical signal to the respective pairof drive electrodes, wherein a geometric configuration of eachrespective combination of a pair of drive electrodes and a respectivemeasurement electrode is selected so that, in the absence of a crack,each respective measured voltage is substantially the same as at leastone other respective measured voltage; and determine whether thematerial includes a crack or other defect based on comparisons betweenthe respective measured voltages; wherein the computing device isfurther configured to, before determining whether the material includesthe crack or other defect based on comparisons between the respectivemeasured voltages, for each respective measured voltage, determining arespective adjusted measured voltage based on the respective measuredvoltage and a respective control voltage associated with the respectivemeasurement electrode; and the computing device is configured todetermine whether the material includes the crack or other defect by atleast determining whether the material includes a crack or other defectbased on comparisons between the respective adjusted measured voltages.59-66. (canceled)